James carried the Heat nearly the entire way until Bosh hit the shot that put Miami ahead for good. Ray Allen followed with four free throws and James finished it off with one more, putting the Heat in position to wrap it up at home Wednesday in Game 5.
James was 16 of 24 from the field and 14 of 19 from the free throw line to match the 49 points he scored for Cleveland against Orlando in the 2009 Eastern Conference finals. He missed his second free throw with 1.1 seconds left.
Joe Johnson scored 18 points for the Nets, who were 15 of 25 from 3-point range in their Game 3 victory but only 5 of 22 in this one. Paul Pierce scored 16 points, while Deron Williams and Shaun Livingston each had 13.
Dwyane Wade scored 15 points on the night his Heat postseason record of 46 points was shattered. Bosh finished with 12.
Miami pulled out a thrilling victory in a game neither team led by double digits and has won at least one road game in 14 straight series, breaking the record set by Chicago from 1991-94.
Brooklyn opened the fourth quarter with six consecutive points to grab an 82-79 edge, and neither team had a bigger margin than that until Kevin Garnett’s two free throws tied it with 2:30 to go.
Pierce, who asked to guard James after Game 1, was on the wrong end of an assault this time.
James and the Heat had shrugged off a couple days of chatter from Pierce, who said the Nets weren’t afraid of the Heat. But things were testy at the start, with first-quarter technical fouls for James, Pierce, Shane Battier and Alan Anderson. Miami started quickly again, making nine of its first 12 shots, and led 27-22 after one behind 12 points from James.
He opened the second on the bench and Brooklyn started with a 9-2 spurt to take its first lead at 31-29 when Andrei Kirilenko converted a three-point play.
James was a force once he returned – especially after a second foul against him seemed to get him more annoyed than any of Pierce’s talking did. He made three baskets in a row to turn a three-point deficit into a three-point lead, and he gave Pierce a glare after a thunderous slam later in the period.
He had 13 points in just 7 ½ minutes of the quarter, and the Heat led 56-49 after making 24 of 38 shots (63 percent) in the first half.
He had 13 straight Miami points in the third, but the Nets were able to get back in the game while the rest of the Heat were being shut out. Brooklyn cut it to one on a few occasions before James made a pair of free throws after coming up with a steal, and Miami led 79-76 going to the fourth.